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New Quantum Error-Correcting Codes from Hermitian Self-Orthogonal Codes over GF(4)

  • Jon-Lark Kim

Abstract

In order to construct good quantum-error-correcting codes, we construct good Hermitian self-orthogonal linear codes over GF(4). In this paper we construct record-breaking pure quantum-error-correcting codes of length 24 with 2 encoded qubits and minimum weight 7 from Hermitian self-orthogonal codes of length 24 with dimension 11 over GF(4). This shows that length n = 24 is the smallest length for any known [[n, k, d]] quantum-error-correcting code with k ≥ 2 and d = 7. We also give a construction method to produce Hermitian self-orthogonal linear codes GF(4) from a shorter length such code.

Keywords

Linear Code Minimum Weight Cyclic Code Association Scheme Quantum Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jon-Lark Kim
    • 1
  1. 1.Department of Mathematics, Statistics, and Computer Science, 322 SEO(M/C 249)University of Illinois-ChicagoChicagoUSA

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